Wednesday, November 30, 2011

We presuppose something like the Principle of Sufficient Reason (PSR) in daily life and science. So there is very good reason to accept something like PSR. But suppose you don't want to accept PSR, maybe because you think it implies the existence of God or maybe because you just think it has counterexamples. What can you do? Here is an option:

The probability that a particular ordinary event, like the coming into existence of a brick or the death of a person, occurs without an explanation is non-zero but very low.

Here are some problems for this. Consider an infinite series of possible events: a brick of weight 2.5kg coming into existence in front of me now, a brick of weight 2.25kg coming into existence in front of me now, a brick of weight 2.125kg coming into existence in front of me now, .... By (1), each of these is very unlikely to happen without an explanation, but there is a non-zero probability for each. Moreover, plausibly, these non-zero probabilities are approximately the same.[note 1] So, we have an infinite number of possible events, each of which has approximately the same non-zero probability. Barring some further dependence story, we should conclude that very likely at least one of these events will happen. But none of these events in fact happened. Repeat the argument with mugs, rocks, etc. None of the analogues there happened. The theory, thus, stands refuted.

If we grant that two bricks can't come into existence in the same place at the same time, the argument can be made stronger. Specify in each event the same location L for the brick. Then we have an infinite number of mutually exclusive events, each of which has approximately the same non-zero probability. And that not only is contrary to observation, but violates the conjunction of the total probability axiom and the finite additivity of probabilities (at least on the right understanding of "approximately the same").

Suppose the theory of bare particularism is wrong. It is plausible that if it's wrong, it's not that its central claims are false, but rather its central claims are nonsense. It is not so much that "There are bare particulars" is false, as that it fails to express anything. Maybe you're not convinced by this particular example, but if so there are probably some others that you'll find convincing. I suspect that many theories in ontology are such that either they're true or they're nonsense, and they aren't all true. Platonism and trope theory are like that, for instance. I'll use bare particularism as my stand-in for such a case.

Yet we have no hesitation in saying things like:

Sally believes that she is partly constituted by a bare particular,

when Sally is a bare particularist. This should trouble us. First of all, analytic orthodoxy holds that in "x believes that s" sentences of this sort (but not in "Sally believes that scientist"!), the "that s" clause refers to the proposition that the sentence "s" expresses.

We could set this orthodoxy aside, and instead of parsing "x believes that s" as predicating a relation of belief between x and the proposition that s, we could take "x believes that" to be a sentential operator. This leads to problems with quantification ("Sally believes some of the things she was just told"), but perhaps those can be solved in some way. But even if we set the orthodoxy aside, we have another problem with (1). We have a sentence that contains a component, outside of quotation marks, that is nonsense, viz., the phrase "bare particular".

The simplest solution to the problem is just to take (1) to be elliptical for some metalinguistic claim like

Sally believes that the sentence "Sally is partly constituted by a bare particular" is true.

Or at least, perhaps, that's the charitable way to take (1). Suppose we do that. Then we have the following oddity. Suppose you and I disagree about whether Sally is a bare particularist. You happen to be a bare particularist yourself, but you doubt that Sally is one. So I say (1) while you say:

It is not the case that Sally believes that she is partly constituted by a bare particular.

Suppose my use of (1) is elliptical for (2). But your use of (3) is surely not elliptical for the negation of (2), since you have no qualms about bare particularism, and you have no reason to make a metalinguistic claim instead of simply attributing a propositional belief to Sally. So your use of (3) is literal, while my use of (1) is elliptical. But then our claims are not directly contradictory. Maybe that isn't a big deal. And maybe your claim, despite your best intentions to the contrary, is in fact metalinguistic, because the reference magnet in the vicinity of your statement is the proposition expressed by (2).

Another problem with reading (1) as (2) is that it is odd to attribute to Sally beliefs about bits of language. What if Sally thinks, for some good or bad reason, that there are no sentences? Again, maybe there is a reference magnet solution.

A hint of a different solution is provided by this post. That post suggests that there is something more fundamental in the mind than beliefs. There are "doxins", which place constraints on what beliefs are to be attributed to one. It may well be that when Sally accepts bare particularism, she isn't believing any proposition like "that she is constituted by a bare particular", but rather she has the doxin expressible by "The credence of the proposition expressed by 'I am constituted by a bare particular' shall be high." If in fact there were such a proposition, this doxin would allow her to be credited with belief in it. There not being any such proposition, we can't credit her with belief. Rather, we credit her with a doxin that carries a false presupposition, viz., that there is a proposition expressed by "I am constituted by a bare particular". The false presupposition, however, isn't a belief. So she can have that doxin while yet not believing in sentences and the like. There would need to be a lot of work done to defend this.

The issue comes up not just for belief. For instance, one might have a desire that "involves a bare particular". Then one would bring in orektins, from the same post.

Monday, November 28, 2011

Al, a single father of young Beth, found himself destitute. To give Beth hope for a future life, he agreed to have Charlie adopt Beth. Charlie was much better off than Al, and as far as Al could tell, was an excellent prospect for fatherhood. Unfortunately, soon after the adoption, Al and Charlie's fortunes reversed. Now Charlie was destitute while Al was well off. Charlie approached Al, suggesting that perhaps Al could re-adopt Beth. But Al said: "She is your daughter and no longer mine, and hence the responsibility is yours." Charlie further asked for financial help for Beth, indicating that he and Beth's health was poor and he (Charlie) could not afford the treatment she needed. Al responded: "Beth is not my daughter. Thus, while her misery has a call on me, it no more has a call on me than the misery of my other people I come in contact with. And I am already sufficiently contributing to the alleviation of the misery of other people, by giving most of my income and available time to various organizations that work with the needy in the city. Moreover, my doing so is financially more efficient. Beth's medical needs are particularly expensive. For the cost of alleviating her misery, I can alleviate the misery of two other poor children. Of course, if Beth were my daughter, her needs would take priority. But she isn't—she's your daughter."

Unless you're a utilitarian, and perhaps even if you are, I think you will share my strong moral intuition that Al is doing something seriously wrong. There are two aspects of this wrong. First, we assume that Charlie has done something good to Al when Al was in need—he took on Beth—and Al is being ungrateful. But we can tweak the story to make Al owe no gratitude to Charlie. Perhaps Al had already done as great a good to Charlie, or perhaps Charlie took on Beth solely for the sake of a tax break and Al was initially mistaken about Charlie's motives.

Second, Al owes more to Beth than he owes to other needy children. Adoption does not, then, completely negate parental duties. In fact, many onerous duties remain with Al, conditionally on Charlie being unable to fulfill them. Beth is not a stranger to Al. I do not know whether we should say that Beth is Al's daughter, but even if she not Al's daughter, the relationship that Al has to her is sufficient to ensure that he is morally responsible for her needs in a way in which he is not morally responsible for a stranger's needs.

But now Al's relationship to Beth is that of merely biological father. This means that the relationship of merely biological father is sufficient to trigger serious duties.

And this, in turn, makes giving sperm to a sperm bank seriously morally problematic. For by so doing, the man is consenting to being the biological father to many children. Given the numbers, it is not unlikely that some of these children will not have their basic needs—whether emotional, intellectual, spiritual or physical—met. In those cases, the donor would have a serious responsibility for meeting these needs. But this is a responsibility he cannot fulfill since he does not even know who these biological children of his are. Therefore, by donating sperm, the donor has consented to a situation where it is likely that he would be failing to meet his serious responsibilities, and where he cannot even seriously try to meet his responsibilities due to confidentiality rules. And that is, surely, morally problematic, even if we bracket all the other problematic aspects of sperm donation.

Notice that any statistics to the effect that adopted children have their needs as well met as biological children will not help here. For what generates the problem I am now discussing are two things. The first is the man is apt to gain many biological children whom he does not know about, adopted into many families, and it is quite probable that at least one of these families is not going to meet the childrens' basic emotional, intellectual, spiritual and/or physical needs. Thus it is rather more probable that he will have responsibilities he is not fulfilling than if he just conceived several children with a woman he was married to, since in the latter case there would only be one family to worry about. Second, in the sperm donation case, the man has responsibilities he cannot even seriously try to fulfill, and that seems a very unfortunate situation.

Saturday, November 26, 2011

In Actuality, Possibility, and Worlds, I attribute to Spinoza the view that no belief is false (though I think i also emphasize that nothing rides on the accuracy of the historical claim). Rather, there are more or less confused beliefs, and in the extreme case there are empty words--words that do not signify any proposition.

I was led to the attribution by a focus on passages, especially in Part II of the Ethics and in the Treatise on the Emendation of the Intellect, that insist that every idea has an ideatum, that of which it is the idea, and hence corresponds to something real. The claim that every idea has an ideatum is central to Spinoza's work. It is a consequence of the central 2 Prop. 7 (which is the most fecund claim outside Part I) which claims that the order and connection of ideas is the order and connection of things, and it is also a consequence of the correspondence of modes between attributes.

These passages stand in some tension, however, to other passages where Spinoza expressly talks of false ideas, which are basically ideas that are too confused to be adequate or to be knowledge (the details won't matter for this post).

I think it is easy to reconcile the two sets of passages when we recognize that Spinoza has an idiosyncratic sense of "true" and "false". In Spinoza's sense, an idea is true if the individual having the idea is right to have it, and it is false if the individual having it is not right to have it (cf. Campbell's "action-based" view of truth, but of course Campbell will not go along with Spinoza's internalism), where the individual is right to have the idea provided that she knows the content, or knows it infallibly. And Spinoza, rationalist that he is, has an internalist view of knowledge, where knowledge is a matter of clarity and distinctness and a grasp of the explaining cause of the known idea.

Hence, Spinoza uses the words "true" and "false" in an internalist sense. But we do not. "True" as used by us expresses a property for which correspondence to reality is sufficient, and "false" expresses a property incompatible with such correspondence. Since every belief has an idea (in Spinoza's terminology) as its content, and according to Spinoza every idea corresponds to reality, namely to its ideatum, it follows that in our sense of the word, Spinoza holds that every belief is true and no belief is false.

The ordinary notion of truth includes ingredients such as that correspondence to reality is sufficient for truth and that truth is a good that our intellect aims at. Spinoza insists on the second part of this notion, and finds it in tension with the first (cf. this argument). But the first part is, in fact, the central one, which is why philosophers can agree on what truth is while disagreeing about whether belief is aimed at truth, knowledge, understanding or some other good.

So, we can say that in Spinoza's sense of "true", it is his view that some but not all beliefs are true. And in our sense of "true", it is his view that all beliefs are true. The sentence "Some beliefs are false" as used by Spinoza would express a proposition that Spinoza is committed to, while the sentence "Some beliefs are false" as used by us would express a proposition that Spinoza is committed to the denial of.

This move of distinguishing our sense of a seemingly ordinary word like "true" from that of a philosopher X is a risky exegetical move in general. Van Inwagen has argued libertarians should not hold that compatibilists have a different sense of the phrase "free will". But I think there are times when the move is perfectly justified. When the gap between how X uses some word and how we use it is too great, then we may simply have to concede that X uses the word in a different sense. This is particularly appropriate in the case of Spinoza whose views are far from common sense, whose philosophical practice depends on giving definitions, and who expressly insists that many disagreements are merely apparent and are simply due to using the same words in diverse senses. (Actually, I also wonder if van Inwagen's case of free will isn't also a case where the phrase is used in diverse senses. Even if so, we should avoid making this move too often.)

Addendum: This reading is in some tension with 1 Axiom 6 which says that a true idea must agree with its ideatum. While strictly speaking, this sets out only a necessary condition for a true idea, and hence does not conflict with what I say above, it is not unusual for Spinoza to phrase biconditionals as mere conditionals. If we read 1 Axiom 6 as a biconditional, then maybe we should make a further distinction, that between the truth of an idea and truth of a believing. We take the truth of a believing to be the same as the truth of the idea (or proposition) that is the object of the believing. But Spinoza distinguishes, and takes more to be required for the truth of a believing. We then disambiguate various passages. The problem with this is that on Spinoza's view, the believing is identical with the idea. But nonetheless maybe we can distinguish between the idea qua believing and the idea qua idea?

Friday, November 25, 2011

My friend Abigail Tardiff sent me this great Advent paper craft [PDF], which I constructed with the kids today, and hung from a folded-up projection screen.

Attached is an easy Advent activity, suitable for kids or grown-ups. Cut on
the lines to make strips, and use a stapler to form the strips into paper
chains, which represent the chains of sin and death. Then each day of
Advent, starting this Sunday, remove one strip and read it. Except for
December 19, which is from the Canticle of Zechariah, they are all Old
Testament prophecies of the coming of the Messiah.
Each strip also has a Jesse Tree ornament (not related to the prophecy) on
it that you may color and cut out, and hang on a branch. The Jesse Tree
tells the history of Salvation, beginning with Creation and ending with
Emmanuel, God With Us. During Advent, we tell our children these stories,
because they tell why we need a Savior, and how God prepared the world for
His coming.
The last seven ornaments are the "O Antiphons" taken from the evening
prayers of those days. You can read about them here:
http://en.wikipedia.org/wiki/O_antiphons. The hymn "O Come, O Come
Emmanuel" is based on the O Antiphons.
Feel free to pass these around. I chose the prophecies, but I kiped
uncopyrighted images from various places on the net.
Happy Advent from the Tardiff family.

According to expressivist views in ethics and aesthetics, sentences like "Murder is wrong" or "The Mona Lisa is beautiful" do not express a proposition, but express some kind of an attitude. I think many propositional attitudes are problematic for expressivists. Here is one that is perhaps not: "Sally thinks murder is wrong." This, the expressivist can say, is a sentence expressing the proposition that Sally has the attitude A, where A is the attitude that she would express by saying "Murder is wrong." But some are much harder:

Sam knows that cheating on exams is wrong.

Alex is unsure whether Picasso's cubist paintings are any good.

The younger Augustine feared that fornication might be wrong.

Dr. Jones hopes that her proposed experiment is morally acceptable.

Mark hopes that the sculpture that he is working on will be beautiful.

Thursday, November 24, 2011

Say that a proposition p is shifty provided that there are worlds w1 and w2 at which p holds, and a proposition q such that q grounds p at w1 but q does not ground p at w2.

A proposition p is non-shifty provided that either it cannot have a ground or there is some proposition q such that p entails that q grounds p.

The proposition that Obama or McCain is president is shifty: in some worlds it is grounded in Obama being president and in others it is instead grounded in McCain being president.

Propositions of the form of the proposition that N exists are non-shifty, if "N" directly rigidly refers to a substance.

Propositions expressed by typical simple subject-predicate sentences are shifty if trope theory is true. For instance, that I am sitting is grounded by the proposition that I have s1, where s1 is the trope of sitting that I actually have, but could have been equally well grounded by the proposition that I have s2, where s2 is some other trope of sitting. On the other hand, if Platonism is true, then sentences whose subject term directly refers and whose predicate expresses a property are going to be non-shifty, as in every world where they are true, they are grounded by some proposition of the form of the proposition that N exemplifies P.

Wednesday, November 23, 2011

Write down a decimal point. Then choose a digit at random, with equal probability 1/10 of each possible digit. Repeat ad infinitum, with all the digits chosen independently. Let X be the number you've written down the infinite decimal expansion of.

Suppose you find out that X is going to be either 1/4 or 1/3. Which of the two is more likely? Answer: 1/4. For there are two ways of getting 1/4: 0.250000... and 0.249999.... But there is only one way of getting 1/3: 0.333333..., and each infinite sequence is equally likely. Thus, intuitively P(X=1/4 | X=1/3 or X=1/4)=2/3. Surprised?

Another interesting fact here. In the technical probability-theory sense, X is uniformly distributed on the interval [0,1]. But in the intuitive sense, it's not. So the technical probability-theory sense does not capture the notion of uniform distribution.

Similarly, the technical probability-theory sense of independence does not capture the intuitive notion of independence. Suppose that a random process uniformly picks out a number Y in the interval [0,1], and suppose you get a dollar if and only if the number is 1/2. Let A be the event that the number picked out is 1/2 and let B be the event that you get a dollar. Then P(A&B)=P(A)=0=P(A)P(B), and hence in the probability-theoretic sense A and B are independent. But intuitively they are far from independent: B is entirely determined by A.

Internalism about truth holds that a belief's being true is a function of things internal to the mind of the believer. Coherentism and Spinoza's extreme rationalism are two kinds of internalisms about truth. Spinoza's argument in the Treatise for the Emendation of the Intellect is basically:

If internalism is not correct, truth is not worth having.

Truth is worth having.

Therefore, internalism is correct.

For (1) to be at all plausible, we need "worth having" to mean intrinsically worth having, and that makes (2) less plausible, though I think (2) remains true. But I deny (1), with or without the qualification, because some things can be intrinsically worth having without being internal or intrinsic to the person. Thus, it is worth having one's friends do well, even though my friends' doing well is not internal or intrinsic to me. Of course my friends' doing well tends to affect me. But not always: my friend could be doing well in my absence, without any contact we me, and that directly makes me better off.

One can also run the argument in terms of knowledge instead of truth. (I think for Spinoza the two come to the same thing! Spinoza thinks knowledge is true belief, but he has high standards for what counts as true belief—beliefs not justified up to Cartesian standards need not apply.)

Suppose that it turns out that, given laws of nature like ours, all sorts of neat self-organization—like what we see in evolution—will follow from most sets of initial conditions. Does this destroy the design argument for the existence of God? After all, that there is complexity of the sort we observe appears to cease to be surprising.

A standard answer is: No, because we still need an explanation of why the laws of nature are in fact such as to enable this kind of self-organization, and theism provides an excellent such explanation.

But what if it turns out, further, that in some sense most laws, or the most likely laws (maybe simpler laws are more likely than more complex ones), enable self-organization processes. So not only is it unsurprising that we would get initial conditions that are likely to lead to self-organization, it is also not unlikely that we would have laws that lead to self-organization. It seems that this undercuts the modified design argument.

But I think there is a further design argument. The result that most, or the most likely, laws would likely lead to self-organization would have to be a very deep and powerful mathematical truth. What explains why this deep mathematical truth obtains? Maybe it follows from certain axioms. But why is it the case that axioms such as to lead to that truth obtain? Well, we can say that they are necessary, but that isn't a very good explanation: it is not an informative explanation. (If it turned out that modal fatalism is true, we still wouldn't be satisfied with explaining all natural phenomena by invoking their necessity. Spinoza certainly wasn't, and this he was right about, though he was wrong that modal fatalism is true.) Theism provides a family of deeper and more informative answers: mathematics is grounded in the nature of a perfect being, and hence it is unsurprising that mathematics has much that is beautiful and good in it, and in particular it is unsurprising that mathematics includes self-organization theorems, since self-organization theorems are beautiful and good features of mathematical reality.

I said that theism provides a family of answers, since different theistic theories give different accounts of how it is that mathematical truth is grounded in God. Thus, one might think, with St Augustine, that mathematical truth is grounded in God's intellect. On the theory I defend in my Worlds book, necessary truths—and in particular, mathematical truths—are grounded in the power of God.

There is, of course, an obvious argument from the beauty of mathematics to the existence of God along similar lines. But that argument is subject to the rejoinder that the beauty of mathematics is a selection effect: what mathematics mathematicians are interested in is to a large degree a function of how beautiful it is. (Mathematicians are not interested in random facts about what the products of ten-digit numbers are.) However, I think the present argument side-steps the selection effect worry.

Saturday, November 19, 2011

In a 2000 article in the Archives of Family Medicine, Larimore argued that because the extremely high effectiveness rate of hormonal contraception is much higher than what one would expect on the basis of its often not very high rate of ovulation suppression, there is very good reason to think a significant portion of the high effectiveness rate is due to preventing implantation of the early embryo. But many women believe that the early embryo is a human being, and hence would take this effect to be a morally unacceptable abortion (and I expect there are additional women who do not take the effect to be utterly morally unacceptable, but for whom such an effect is nonetheless a significant reason against the use of the contraceptive method). Since patient autonomy requires that the patient be informed of those aspects of treatment that are salient given the patient's values and moral beliefs, the physician's duty in the case of such women is to inform the women of the risks of prevention of implantation. Because a physician may not know whether a particular woman consider this factor relevant, Larimore suggests that a physician can say something like: "Most of the time, the pill acts by preventing an egg from forming. This prevents pregnancy. However, women on the pill can still sometimes get pregnant. Some doctors think that the pill may cause the loss of some of these pregnancies very early in the pregnancy, before you would even know you were pregnant. Would knowing more about this possibility be important to you in your decision about whether to use the pill?"

Even bracketing the question whether contraception and abortion are morally permissible, Larimore is right about what is required what the current consensus on patient autonomy and informed consent. I've had a look at the titles and often abstracts of the 55 papers listed as citing Larimore's, and surprisingly none of them appears to be an argument to the contrary (though maybe some contain such an argument in their body). One interesting recent study of women in Western and Eastern Europe found that only 2% can correctly identify all the mechanisms of oral contraceptives and the IUD (for which the postfertilization effect is probably even greater), but that 73% said that their healthcare provider should inform them about effects that occur after fertilization even when these effects are before implantation. So not only is the information salient to many women, it is information that many women want.

It seems to me that pro-choice physicians should be impressed by the need to obtain informed consent for such postfertilization effects insofar as a significant part of the reasoning for the pro-choice position involves considerations of women's autonomy.

Friday, November 18, 2011

It is only appropriate punish that which harms someone or something else, or is intended or sufficiently likely to do so.

(If one thinks that exposing someone to a sufficient probability of harm is itself a harm, one can simplify this. Note also that what counts as sufficiently likely is relative to the degree of punishment and degree of harm. Doing something that has a one in a million chance of causing me a hangnail is probably not deserving of punishment, except maybe of the most trivial sort, but doing something that has a one in a million chance of blowing up New York may well deserve serious punishment—cf. Parfit on small chances.)

I shall argue against this principle. Recall Mill's very plausible insistence that:

Being subject to social opprobrium is a kind of punishment.

(And one often would rather pay a hefty fine than be subject to social opprobrium, so it can be a heavy punishment.) Now observe:

Some irrational beliefs are appropriately subject to social opprobrium even though they harm no one else, are not intended to harm anyone else and are not sufficiently likely to do so.

For instance, consider someone's really crazy conspiracy theoretic beliefs which were formed irrationally, out of a desire to be different, rather than out of an honest investigation of the truth, and suppose that this is someone whom no one is likely to believe, and hence someone harmless in these beliefs. Or consider the racist beliefs of someone who is too prudent to ever act on them because she does not wish to risk social disapproval.

Therefore:

It can be appropriate to punish something that harms no one else, and is neither intended nor sufficiently likely to do so.

Now, one can get out of this consequence if one makes some sort of a communitarian assumption that no man is an island, that one person's irrationality is a constitutive part of the community's being thus far irrational, and is eo ipso harmful to other members of the community even if they do not themselves follow this irrationality, since now they are made to be participants in a community that exhibits this irrationality. But if one allows such "extended harms", then the principle (1) becomes uninteresting. Likewise, if one brings in "extended harms" to God, where God is said to be harmed in an extended sense provided that one acts against his will.

Could one turn this around and make it an argument for tolerance of irrationality? This would involve insisting on (1) and concluding that harmless irrationality should not be the subject of opprobrium. Yet such opprobrium seems to be an important part of what keeps us rational, and it seems obviously appropriate, especially when the irrationality is a result of the agent's moral failings.

Thursday, November 17, 2011

A couple of days ago, an interesting thing happened. Our Department secretary emailed me, in my capacity as Graduate Director, to find out if student A was eligible for an MA degree. When I got to checking, I confused student A with student B, and checked that student B is eligible. Then I emailed our secretary and said that it was all fine. Consequently, I assume, she formed a justified belief that student A was eligible for an MA degree. But this justified true belief wasn't knowledge, since it relied on my testimony, and I did not know whether A was eligible for an MA.

Shortly thereafter, I realized my mistake. I then checked whether A was eligible, and found that indeed A was eligible. Next, I wondered what to do. Our secretary did not know that A was eligible. But she did, as a result of my mistake, have a justified and, as it happened, true belief. I could easily turn her justified true belief into knowledge by emailing her about what happened.

If knowledge has a value over and beyond the value of justification and truth, then I had a reason to email her. But it seems like it would be pointless to send a correction email under the circumstance (or at least, giving her knowledge would not be a point). And, if it would be pointless, then it seems that there is no value over and beyond the value of justification and truth.

However, a colleague suggests that perhaps the right interpretation of the situation isn't that there is no value in knowledge over and beyond justification and truth, but that there is so little value that it is outweighed by the disvalue of bothering a very busy person with yet another email.

Wednesday, November 16, 2011

Say that the fecundity of a claim in a logically interconnected text, like Spinoza's Ethics, is the number of claims that logically depend on it. Using the Tredwell adjacency data, I sorted the claims in Spinoza's Ethics in order of decreasing fecundity. We can measure the fecundity in percentages: the percentage of the claims that depend on the given claim.

The result is here. (The explanations of what the items are are here, from Tredwell.) Fecundity is a measure of how fundamental a given claim is to the system.

The twelve most fecund claims, with their number of dependants, are:

1A04: 300 (77.3%)

1D03: 296 (76.3%)

1D04: 295 (76.0%)

1D05: 292 (75.3%)

1A06: 291 (75.0%)

1A01: 291 (75.0%)

1P01: 290 (74.7%)

1A05: 290 (74.7%)

1P04: 290 (74.7%)

1P02: 289 (74.5%)

1P03: 289 (74.5%)

1P05: 289 (74.5%)

Unsurprisingly, they're all from Part I of the Ethics, and unsurprisingly the first six are all axioms or definitions.

The most fecund is Axiom 4, that the cognitio (understanding?) of the effect depends on the cognitio of the cause, which, through Spinoza's overreading of it (it sounds like a weak claim, and that's why we are tempted to agree, but in fact it is a strong claim), becomes the root of the epistemologically central 2 Proposition 7, which says that the order and connection of things is the order and connection of ideas. In fact, it is largely through this 2P07 that Axiom 4 gets its fecundity: 2P07 has a fecundity of 60%, and assumes nothing other than 1A04.

The most fecund derived claim is 1 Proposition 4, that distinct things must differ in attribute or mode.

Unsurprisingly, the ontological argument is central: the fecundity of 1 Proposition 11, that God exists, is 73%.

The most fecund claim from outside of Part 1 is the aforementioned 2 Proposition 7, whose centrality cannot be denied.

There are 103 propositions that have zero fecundity.

Axiom 2 of Part I has zero fecundity in the database I am using, as do 5A02 and 2A08. Due to the limitations of my method, axioms and definitions with zero fecundity don't appear in the results I linked to, though I may fix that eventually. The case of Axiom 2 of Part I interesting and surprising, since it basically states Spinoza's version of the Principle of Sufficient Reason. My feeling is that it is implicitly used all over the place.

The least fecund axiom that actually gets used is 5A01, about contrary actions, which has only one dependent. The next, somewhat more fecund axiom is 4A01, at 4% fecundity, which says that for any thing, there is a stronger thing which can destroy it.

Surprisingly to me, the least fecund axiom from Part 1 is 1A03, at 8%, which basically affirms that causation is deterministic. This may initially suggest that Spinoza's causal determinism is not as central to his thought as it is normally thought to be. But that might be too quick, because I suspect that much if not all of the deterministic import of 1A03 is found in 1A04, especially as interpreted by 2P07 and with the understanding the the logical connections between ideas are always entailment relations.

R. F. Tredwell has the data for generating a logical dependency graph of Spinoza's Ethics. I converted the data into DOT format so it can be used with GraphViz, and used GraphViz's dot to generate visual representations.

Potentially more interesting are the individual graphs of the five parts of the Ethics. Each graph includes the items from the part in question, as well as the dependencies from earlier parts. (Again, there is a "View original" link for each which downloads the jpeg file.)

According to some presentist theories of time, facts about the future are grounded in facts about the present and in the laws of nature. What grounds the fact, if it is a fact, that tomorrow the sun will rise is that the present conditions together with the laws of nature entail that the sun will rise tomorrow. Alan Rhoda played with a similar view in regard to the past: facts about the past are grounded in facts about God's present memories.

Suppose determinism holds and there is an initial time t0. Let L be the laws. Then we can imagine a view which we might call initialism in the place of presentism. According to initialism, facts about what happens at a time t>t0 reduce to facts about what the laws are and what the initial conditions are. More precisely, if I is the initial conditions of the world at t0, according to initialism, what it is for a state of affairs to obtain at a time t>t0 is for I and L to jointly entail that it obtains at t. Thus, what it is for there to be humans in the world is for the world to have had initial conditions and laws such as to guarantee the arising of humans.

According to initialism, none of us are substances, because facts about our existence reduce to facts about the initial conditions and laws. In Spinozistic terminology, we are modes of laws and initial conditions or of whatever grounds the laws and initial conditions.

Initialism has some obvious problems. It assumes that determinism holds and that there is an initial time t0. But determinism is in tension with quantum mechanics, and probably the best interpretation of the Big Bang is that although the universe has finite age, there was no initial moment.

There is a strong resemblance between initialism and Spinoza's metaphysics. To make the resemblance closer, we will make some modifications.

Modification 1: Take time to discrete. Thus, there is a finite number of moments of time between t0 and the present. If we do this, we can get a nested view closer to Spinoza's. Instead of reducing the conditions at time tn to the laws and the conditions at t0, we reduce them to the conditions at tn−1 and the laws. Now our present time slices are modes of modes of ... modes of the initial conditions and laws.

The second move we can make is to remove the initial time t0. Instead, there is a doubly infinite sequence of times ...,t−2,t−1,t0,t1,t2,.... How things are at each time reduces to the laws and how they were at the preceding time. Thus, in Spinozistic terminology, we are modes of modes of modes of ....

The third move is to reintroduce something outside of the whole sequence of modes, in which the sequence of events is grounded. After all, the idea of a sequence of modes without any substance seems absurd. One move would be to take that which is outside the sequence to be the lawmaker of L—that entity in virtue of which L is law, the truthmaker of the proposition that L is law. We may perhaps call this entity "Natura Naturans", nature naturing, or if we are pantheistically inclined like Spinoza, "Deus sive Natura" (though the latter identification would be taking a stand on whether Spinoza's Deus is Natura Naturans or the whole shebang of nature, in favor of the former). If we like, we can call the mereological sum of the modes "Natura Naturata", nature natured. The Natura Naturans, then, is the substance of which the temporal modes are ultimately (though with an infinite chain intervening) are modes.

The final move, to make the view be more like Spinoza's, is to take out the reference to times. Instead, we just have a sequence of entities—objects and/or events—that are each reduced to previous ones.

I think one puzzle about this view is how the Natura Naturans is related to the sequence of temporally qualified, "determinate", modes. We could take this relationship to be one of reduction once again: the whole infinite sequence of times reduces to the laws. This fits with much of what Spinoza says. It is, however, in some tension with Spinoza's idea that from the idea of God qua eternal, and it is this which seems to fit best with this eternal lawmaker, temporally determinate facts do not follow.

This exegetical difficulty can perhaps be overcome.

Here is one way. Accept a relationist B-theory of time, and then say that something is determinate insofar as we can delineate the times of its beginning and end. But on a relationist B-theory, sub specie aeternitatis, we just have a doubly infinite sequence without time-as-a-container, and no non-relative, non-arbitrary way of identifying times like "November 15, 2011". Of course, we can stipulate names for beginning and end times of some events, and then with this stipulative delineation in hand, we can delineate temporally when other events will happen. Thus, if a match struck just before noon, it will come on fire just after noon. Thus, to derive facts about when events happen we need facts about when other events happen. We cannot derive when-facts from eternal laws. Spinoza is clear on his view that times are the product of human beings divisions of duration.

If all there was to being a determinate mode was having a beginning and end time, I think that would be a satisfactory answer. But I think temporally determinate modes may be prior on his view to times. Perhaps, though, his thought is this. What we can derive from L is the whole sequence of things, but considered as an undivided sequence, and all divisions and delineations in the sequence are due to us. And from a delineated cause—say, a match's being struck, which is delineated from what comes before (the movement of the match) and what comes after (the fire)—there can be derived a delineated effect. Again, on this reading, the division in the modes is arbitrary.

Actually, I am not sure that Spinoza's mode-to-haver relationship is reductive. But I think it gives an illuminating reading.

Friday, November 11, 2011

I don't think you have much hope of having a distinction between treatment and enhancement unless you have the notion of the normal state or proper function of the human body. I previously thought we want a distinction between treatment and enhancement for such purposes as figuring out what the task of the physician as such is and what requests from the patient the physician has a right to turn down flat. For instance, a physician who receives a request to remove a cancer, and who judges that removal of the cancer is feasible, safe and ethically permissible, has a medical duty to either remove the cancer or refer to someone else. On the other hand, a physician who receives a request to pierce a patient's ears for earrings, even though she no doubt judges this to be feasible and ethically permissible, has no medical duty to perform the procedure or refer to someone else, since it is not a medical treatment.

But a new kind of case seems to me to make the distinction even more pressing, and this is cases where it is not possible to ask the patient's consent. Suppose that in the middle of heart surgery, the surgeon notices an old bullet lodged near the heart. The bullet does not impair the heart's functioning, so the patient's consent to the heart operation does not extend to the bullet. But it is intrinsically morally permissible for the surgeon to remove the bullet if she reasonably judges that doing so is good for the patient (of course, there may be laws and regulations that prohibit this, in which case it will be extrinsically impermissible). On the other hand, if a brain surgeon removing a cancer from someone's brain reasonably judges, on the basis of the latest research, that moving a few neurons around will make the subject super-fast at arithmetic with large numbers, that is unacceptable. Likewise, if in the course of a Caesarian the physician notes that the tubes could be tied and judges that the patient would be better off not getting pregnant, that too is unacceptable, whether or not consensual sterilization is permissible (this is, alas, not a hypothetical case).

One can try to handle this with "presumed consent", but that's kludgy, and probably doesn't work. Presumed consent from an unconscious suicidal patient for emergency treatment following the attempted suicide is going to involve dubious counterfactuals, like asking what the patient would want if the patient were fully sane (there might be no fact of the matter about this), and, besides, you probably can't make sense of "sane" without the concept of normalcy. Moreover, we can imagine cases where one can presume that the patient would consent if asked, but the action is still wrong. For instance, one may well know of many patients that they would agree to have a gift of diamonds worth millions sewed into them as a part of surgery, if they were going to be later notified and could have the diamonds safely removed through another surgery and if there was no other way for them to be given the diamonds. But to sew in the diamonds as part of heart surgery, without having sought the patient's consent, is morally impermissible--or at least it's bad medicine.

Thursday, November 10, 2011

Here are some thoughts on St Matthew's version of the Lord's Prayer, many taken from or loosely inspired by things people said at our Department Bible study yesterday (though what I say should not be taken as representing anything like a consensus). First, my translation:

9Our father, who art in heaven:
Thy name be sanctified,10thy kingdom come,
thy will come to pass,
as in heaven so on earth.11Give us daily our supersubstantial [epiousion] bread.12And forgive us our debts
as we forgive our debtors.13Do not bring us to a trial,
but instead deliver us from the evil one [tou ponerou]. (Matthew 6:9-13)

The overall theme is that of the earthly and the heavenly, with the earthly being brought in conformity with the heavenly, by our own activity and that of our father. "As in heaven so on earth", I take it, applies to each: "thy name be sanctified", "thy kingdom come" and "thy will come to pass." Each of these three is simultaneously a request and a personal commitment to the indicated task, and in each case the act of praying is already partly constitutive of the prayed-for result: by praying these we sanctify our Father's name, make his kingdom present and do his will.

Implicit behind all three requests is an image of the majesty of God enthroned above the heavenly hosts who sanctify his name and bring his will to pass--and yet this King of the Universe is also our father.

The prayer is enveloped between the "father" (the first word in the Greek--while in Aramaic and Hebrew, "our father" would be one word) and "the evil one" at the end. This involves reading tou ponerou as "the evil one" (masculine) rather than as generically "evil" (neuter). This is supported the neatness of the resulting envelope structure, the central focus in the prayer on the beyond-earthly significance of our actions, as well as the implicit imagery of the angels of the heavenly host.

The central request is for our epiousios bread. We really don't know how to translate the word. A leading view is that it is the bread for the day to come. But it could also be the bread needed for our existence or ousia, the bread for the life to come, or, following St Jerome's Latin calque, the supersubstantial bread. In any case, the Church has traditionally taken a Eucharistic reading of the text, and such a reading makes the tendency of the earthly towards the heavens come to a head here: we sanctify his name and do his will just as the angels do, and here we boldly ask for the bread of angels, the new manna, the earthly bread made into the body of him who became flesh for us, the bread that is literally the Logos of God on which man lives (cf. Jesus' struggles with the evil one two chapters back in Matthew). At the same time, this reading should not rule out--and indeed the heavenly-earthly parallelism structure is very friendly to it--that this is also a request for what we need for our earthly lives from our heavenly royal father.

In verse 12, we have a switch from the positive to the negative aspects of transforming the earthly into the heavenly. The debt of our sin to God imposes on us an obligation we cannot pay and yet paying which is essential to the coming of his kingdom on earth. We boldly ask that it be forgiven, because (seemingly a non sequitur, but yet God in love for our children makes it follow) of our forgiving the debts of our debtors. It is neither good to be debtor nor creditor, and here by ceasing to be creditors we cease to be debtors. The forgiveness here is in the first instance a loosing or a release. The essential effect is normative, that the debtor is quit of the debt. Of course, when we forgive another, the essential effect is not all that we are called to: we are called to an affective component--we should feel as if the person who sinned against us is no longer in debt to us--and sometimes to a concrete reaching out to heal the relationship. Likewise, God's forgiveness heals us, and gives us the grace to avoid incurring further indebtedness, as indicated by the next verse.

The trials of verse 13 may well include ordinary temptations, but it is also plausible that the text is specifically talking of the trials of persecution and torture. We pray that our father not bring us there, and at the same time we should not deliberately take ourselves there either (there is the scary story in Eusebius about the early Christian who from bravado turned himself in to the Romans--and then broke down and apostasized). Finally, we are reminded that we do not struggle against mere flesh and blood, but that persecutions and temptations are the work of infernal intelligence, like the devil that Jesus fought two chapters back.

Wednesday, November 9, 2011

If naturalism is correct, a desire to be morally perfectcannot be fulfilled for humans.

If a desire cannot be fulfilled for humans, it is not morally required for humans.

Therefore, naturalism is not correct.

This argument provides a schema for a family of arguments. One obtains different members of the family by replacing or disambiguating the underlined terms in different ways.

If one disambiguates "naturalism" as physicalism (reductive or not), one gets an argument against physicalism (reductive or not). If one disambiguates "naturalism" in the Plantinga way as the claim that there is no God or anybody like God, one gets an argument for theism or something like it. Below I will assume the first disambiguation, though I think some versions of the schema will have significant plausibility on the Plantingan disambiguation.

One can replace "morally required" by such terms as "normal", "non-abnormal" or "required for moral perfection".

One can replace "to be morally perfect" by "for a perfect friendship", "to be perfectly happy" or "to know with certainty the basic truths about the nature of reality" or "to know with certainty the basic truths about ethics" or "to have virtue that cannot be lost". While (1) as it stands is quite plausible, with some of these replacements the requiredness versions of (1) become less plausible, but the "non-abnormal" version is still plausible.

Probably the hardest decision is how to understand the "cannot". The weaker the sense of "cannot", the easier it is for (2) to hold but the harder it is for (3) to hold. Thus, if we take "cannot" to indicate logical impossibility, (2) becomes fairly implausible, but (3) is very plausible as above.

I would recommend two options. The first is that the "cannot" indicate causal impossibility. In this case, (3) is very plausible. And (2) has some plausibility for "moral perfection" and all its replacements. For instance, it is plausible that if naturalism is true, certain knowledge of the basic truths about the nature of reality or about ethics is just not causally available. If, further, moral perfection requires certainty about the basic truths of ethics (we might read these as at the normative level for this argument), then moral perfection is something we cannot have. And if we cannot have moral perfection, plausibly we cannot have perfect friendship either. Likewise, if naturalism is true, virtue can always be lost due to some quantum blip in the brain, and if moral perfection requires virtue that cannot be lost, then moral perfection is also unattainable. And perfect happiness requires certain knowledge of its not being such as can be lost. Maybe, though, one could try to argue that moral perfection is compatible with the possibility of losing virtue as long as the loss itself is not originated from within one's character. But in fact if naturalism is true, it is always causally possible to have the loss of virtue originate from within one's character, say because misleading evidence could come up that convinces one that torture is beneficial to people, which then leads to one conscientiously striving to become cruel.

The second option is that the "cannot" is a loosey-goosey "not really possible", weaker than causal impossibility by not counting as possible things that are so extraordinarily unlikely that we wouldn't expect them to happen over the history of humankind. Thus, in this sense, I "cannot" sprout wings, though it seems to be causally possible for my wavefunction to collapse into a state that contains wings. Premise (2) is now even more plausible, including for all the substituents, while premise (3) still has some plausibility, especially where we stick to the "morally required" or "required for moral perfection", and make the desire be a desire for moral perfection.

If I am counting correctly, if we keep "naturalism" of the non-Plantingan sort, but allow all the other variations in the argument, we get 48 arguments against naturalism, though not all independent. Or we can disjoin the conjunctions of the premises, and get an argument with one premise that is a disjunction of 48 conjunctions of three premises. :-)

People do things that seem to be irrational in respect of maximizing expected utilities. For instance, art collectors buy insurance, even though it seems that the expected payoff of buying insurance is negative—or else the insurance company wouldn't be selling it (some cases of insurance can be handled by distinguishing utilities from dollar amounts, as I do here, but I am inclined to think luxury items like art are not a case like that). Likewise, people buy lottery tickets, and choose the "wrong" option in the Allais Paradox.

Now, there are all sorts of clever decision-theoretic ways of modeling these phenomena and coming up with variations on utility-maximization that handle them. But rather than doing that I want to say something else about these cases.

Why is it good to maximize expected utilities in our choices (and let's bracket all deontic constraints here—let's suppose that none of the choices are deontically significant)? Well, a standard and plausible justification involves the Law of Large Numbers [LLN] (I actually wonder if we shouldn't be using the Central Limit Theorem instead—that might even strengthen the point I am going to make). Suppose you choose between option A and option B in a large number of independent trials. Then, on moderate assumptions on A and B, the LLN applies and says that if the number of trials N is large, probably the payoff for choosing A each time will be relatively close to NE[A] and the payoff for choosing B each time will be relatively close to NE[B], where E[A] and E[B] are the expected utilities of A and B, respectively. And so if E[A]>E[B], you will probably do better in the long run by choosing A rather than by choosing B, and you can (on moderate assumptions on A and B, again) make the probability that you will do better by choosing A as high as you like by making the number of trials large.

But here's the thing. My earthly life is finite (and I have no idea how decision theory is going to apply in the next life). I am not going to have an infinite number of trials. So how well this LLN-based argument works depends on how fast the convergence of observed average payoff to the statistically expected payoff in the LLN is. If the convergence is too slow relative to the expected number of A/B-type choices in my life, the argument is irrelevant. But now here's the kicker. The rate of convergence in the LLN depends on the shape of the distributions of A and B, and does so in such a way that the lop-sided distributions involved in the problems mentioned in the first paragraph of the paper are going to give particularly slow convergence. In other words, the standard LLN-based argument for expected utility maximization applies poorly precisely to the sorts of cases where people don't go for expected utility maximization.

That said, I don't actually think this cuts it as a justification of people's attitudes towards things like lotteries and insurance. Here is why. Take the case of lotteries. With a small number of repetitions, the observed average payoff of playing the lottery will likely be rather smaller than the expected value of the payoff, because the expected value of the payoff depends on winning, and probably you won't win with a small number of repetitions. So taking into account the deviation from the LLN actually disfavors playing the lottery. The same goes for insurance and Allais: taking into account the deviation from the LLN should, if anything, tell against insuring and choosing the "wrong" gamble in Allais.

Maybe there is a more complex explanation--but not justification--here. Maybe people sense (consciously or not—there might be some evolutionary mechanism here) that these cases don't play nice with the LLN, and so they don't do expected utility maximization, but do something heuristic, and the heuristic fails.

Monday, November 7, 2011

Here's a fun set of experiments to do with kids. You need two pennies, two nickels and a voltmeter that can show voltages of the order of 10-50 millivolts. I used this cheap one. Probes with alligator clips make the experiments easier (I bought some alligator clips in Walmart's automotive section and soldered them on probes from an old multimeter), but you can do it with straight probes, too (in that case, replace "attach the probes" should be replaced with "touch the probes").

Experiment 1: Attach the probes to a penny and a nickel, respectively. Set the voltmeter to a scale that will show things of the order 10-50 mV (I used a 2000 mV scale). Have a volunteer hold the penny in one hand and nickel in the other. Measure the voltage. Ideally, the probes should be touching the coins, not the hands. I was getting about 15-35 mV, depending on which kid was holding the coins. If you're not getting much, maybe moisten the volunteers' hands. Then vary the coin combinations.

Experiment 2: Attach the probes to a penny and a nickel, respectively. Get two volunteers, and have each hold one of the coins. Make sure the volunteers aren't touching. Measure the voltage. Should be zero or very low (if the floor is conducting a bit). Now have them hold hands. There should be a very gratifying jump in voltage from this hand-holding switch! Note the voltage (it may take a while for it to stabilize).

Experiment 3: Set it up like for Experiment 2, but instead of having the volunteers hold hands, have the volunteer who is holding the penny hold out the other hand, palm up and outstretched. Put a nickel and a penny on that palm, with the nickel above, in such a way that the penny doesn't touch the skin (so don't put them in the middle of the palm, but maybe more on the heel; or maybe use a quarter instead of the nickel). Then instead of having the volunteers hold hands, have the second volunteer--the one holding the nickel--press a thumb from the free hand onto the penny that is on top of the nickel, being careful to make sure the penny doesn't make contact with the first volunteer's skin. Compare the voltage to that in Experiments 1 and 2. You've now got a two-cell human battery!

There are lots of fun variables to vary. Change the size of the volunteers. Wet or dry hands. See if drinking a lot makes a difference. See if temperature makes a difference (indoor vs. outdoor, say).

You can also do this, which I haven't tried, but it should work. What I did try, though, was this (though I used lime juice), which very gratifyingly powered an LED. When it went out, adding more lime juice turned it back on.

Saturday, November 5, 2011

You get a book, with the title page and covers missing, and you start to read. After a while, you realize it's a book of fiction. Some time later, you realize it's a book of science fiction. Then you realize it's a book of hard science fiction. The more you learn about the genre of the book, the better you can make predictions about what is to come in the book. Prior to learning it's a book of science fiction, you thought you could make inferences based on the present limits of technology, but after you learned that it was science fiction, these inferences became bad. And once you've learned that it's hard science fiction, you become able to make inferences on the basis of most if not all of the laws of nature that we know of.

The physical universe is God's book. It took us a while—namely, until around the late middle ages—to figure out the genre, namely that the genre is deeply mathematical. Once we figured out the genre, it became very easy to make fast progress understanding the book and making predictions.

A good work of art tends to have a deep unity of genre in it (which is compatible with all sorts of complexity). There is, thus, good reason to suppose that once we've identified the genre of the parts of the work we have seen, something generically similar will follow.

Modern science, thus, grasped an important aspect of God's artistic plan for the universe, as in Galileo's remark about the book of nature being written in the language of mathematics. It is a difficult question whether the practice of science can rationally stand without such theistic underpinnings.

Friday, November 4, 2011

I suspect that many philosophers would rather have their work be criticized as being morally perverse than as being stupid or merely tritely repeating unoriginal claims from the literature. At least, I find myself with feelings like that. Does this preference expose a deep vice in me?

I am not sure. It may simply be that I trust other philosophers' judgment as to what is stupid or in the literature more than I trust their moral judgment. At least, if the moral perversity criticism came from one of the philosophers whose moral judgment I really trusted, the judgment would worry me a lot more. But I am not sure it would still worry me as much as a judgment of stupidity or unoriginality from someone of comparable epistemic authority.

Thursday, November 3, 2011

Love contains three aspects: appreciation, benevolence and a striving for union. Suppose that we are supposed to love all human beings. In a secular context, each of the three aspects of love threatens to make the love in many cases rather anemic. It is only in a context like that of Judaeo-Christian theology that one can have a love that is both rich and universal. For let's consider the aspects severally.

Appreciation: Unless we have some picture of the human being as in the image and likeness of God, it is difficult to see that much to appreciate in a Mengele. This can perhaps be overcome if one has a robust enough notion of human nature, though perhaps that is just bringing in the image and likeness of God in a hidden way.

Benevolence: It is possible to will the good to all, as this involves a merely dispositional property. But a merely dispositional beneficence is an anemic sort of benevolence. In a religious context, however, the benevolence can act as a genuine beneficence through prayer and something like the communion of the saints.

Unitiveness: While appreciation and benevolence by themselves imply a kind of union, love's striving for union goes beyond these. But in a secular context one can't really go much beyond these in many cases. First, there is the problem of those who appear completely morally corrupt, with whom a further union would be morally problematic. In a religious context, however, the striving for union connects with eschatology. Every individual human on earth is someone with whom we can strive for eternal union in heaven (even if we believe that we won't achieve this union in every case). Second, and even more seriously, there is the problem of the billions of people with whom we simply cannot have a deeper union, because life is too short and their lives do not intersect our lives enough (for a more radical case, one might cite people in the distant past or distant future!) Again, this is overcome in a religious context, often by a potential for liturgical union—in liturgy, we are importantly united with people all over the world participating in the same liturgy—and always by a striving for a union in heaven that is prefigured by the liturgical union.

An interesting question is how the unitiveness will be realized in heaven between those who are in heaven and those who are in hell. I think here there is a kind of liturgical union, in that both those who are in heaven and those who are in hell are united in praise of God: those in heaven deliberately and explicitly so, while those in hell praise God by the value of their existence and the divine justice they exemplify. This is probably a hard saying.

If the above is right, then the duty of universal love can only fully come into its own in a religious context.

Wednesday, November 2, 2011

Leibniz tells us that bodies are phenomena. He also tells us that phenomena are modes of monads. Now, the modes of monads are appetites and perceptions. But appetites and perceptions are identity-dependent on the monad that they are appetites and perceptions of. Your appetite or perception may be very much like mine, but it is numerically distinct from mine. But this seems to imply that the moon you see and the moon I see are numerically distinct. For the moon you see is a mode of you, and hence identity-dependent on you, while the moon I see is a mode of me, and hence not numerically distinct with the moon that is identity-dependent on you.

Something must go. The identity dependence of modes on the monad is central to Leibniz's argument against inter-modal causation: he insists that the same mode cannot have a leg in each of two monads. My suggestion is that what Leibniz should say, and maybe what he really thinks, is that real phenomena, like the moon, aren't modes of monads in the narrow sense that implies identity dependence, but are grounded in monads, and in that sense are modes of monads in the broad sense. Consider "the committee's opinion." This is grounded in the committee members' minds, but it is not identity-dependent on any one committee member: individual committee members can change their view while the committee is still "of the same mind."

Here is one way to make this go. The moon is a phenomenon and it has a two-fold ground. One part of the ground are monads having "lunar perceivings", like the one I had last night when looking through the telescope, and like the one I am now, according to Leibniz, unconsciously having. But the moon isn't just a lunar perceivings, because your lunar perceiving is distinct from my lunar perceiving. The other part of the ground is what unifies the lunar perceivings in different monads, and that is the monads that are elements (in Robert Adams' phraseology) of the moon. Your lunar perceiving represents the same lunar monads as my lunar perceiving does.

For Leibniz, as for Aristotle, being and unity are interchangeable. To have being, bodies need a source of unity. On this reading, there are two sources of unity in the moon: first, the perception of a monad, say you or me, unifies the many lunar monads that are being perceived; second, the lunar monads unify the perceptions of the many monads. There is no vicious circularity here.

This significantly qualifies Leibniz's alleged idealism. It sounds idealist to say that bodies are phenomena. But they aren't just any phenomena, they are "well founded" phenomena (to use Leibniz's phrase), and a part of what constitutes them into the self-identical phenomena that they are is the monads that are appearing in the appearance.

The above brings together ideas I got from at least two of our graduate students. Another move suggested by one of them is to take the unification of the lunar perceivings to happen through the complete individual concept of the moon which is confusedly found in all of the lunar perceivings. I think this, too, is a possible reading of Leibniz, but I think it makes for poorer philosophy, since I don't think there is any complete individual concept of the moon found in all lunar perceivings, except in the way that the concepts of causes are, by essentiality of origins, found in the effects.

Tuesday, November 1, 2011

Consider two different methods for what to do with the opinion of someone more expert than yourself, on a matter where both you and the expert have an opinion.

Adopt: When the expert's opinion differs from yours, adopt the expert's opinion.

Caution: When the expert's opinion differs from yours, suspend judgment.

To model the situation, we need to assign some epistemic utilities. The following are reasonable given that the disvalue of a false opinion is significantly worse than the value of a true belief, at least by a factor of ~2.346 in the case of confidence level 0.95, according to the hate-love ratio inequality.

Utility of having a true opinion: +1

Utility of having a false opinion: approximately -2.346

Utility of suspending judgment: 0

Given these epistemic utilities, we can do some quick calculations. Suppose for simplicity that you're perfect at identifying the expert as an expert (surprisingly, replacing this by a 0.95 confidence level makes almost no difference). Suppose the expert's level of expertise is 0.95, i.e., the expert has probability 0.95 of getting the right answer. Then it turns out that Adopt is the better method when your level of expertise is below 0.89, while Caution is the better method when your level of expertise is above 0.89. Approximately speaking, Adopt is the better method when you're more than about twice as likely to be wrong as the expert; otherwise, Caution is the better method.

In general, Adopt is the better method when your level of expertise is less than e/(D-e(D-1)), where e is the expert's level of expertise and D is the disutility of having a false opinion (which should be at least 2.346 for opinions at confidence level 0.95). If your level of expertise is higher than that, Caution is the better method.

Here is a graph (from Wolfram Alpha) of the level of expertise you need to have (y-axis), versus the expert's level of expertise (x-axis), in order for adopting Caution rather than Adopt to be epistemic-decision-theory rational, where D=2.346.

Here is a further interesting result. If you set the utility of a false opinion to -1, which makes things more symmetric but leads to an improper scoring rule (with undesirable results like here), then it turns out that Adopt is better than Caution whenever your level of expertise is lower than the expert's. But for any utility of false opinion that's smaller than -1, it will be better to adopt Caution when the gap in level of expertise is sufficiently small.
If you want to play with this stuff, I have a Derive worksheet with this. But I suspect that there aren't many Derive users any more.

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I am a philosopher at Baylor University. This blog, however, does not purport to express in any way the opinions of Baylor University. Amateur science and technology work should not be taken to be approved by Baylor University. Use all information at your own risk.